Some combinatorial and symbol manipulation programs in group theory

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This chapter discusses some combinatorial and symbol manipulation programs in group theory. A program has been written that determines the generators and relations of all the subgroups of a finite soluble group. The program finds the subgroups using the same method as Neubüser with the difference that as a subgroup of order d is found the generators and relations of all possible groups of order d are checked through to find a set of generators and relations for the subgroup. As the program is restricted to groups of order less than 400 by machine considerations, all the possible groups of order less than 200 need to be known. The program reads the generators and relations of the given group and finds a faithful permutation representation using coset enumeration.